Download Student Workbook Options

Fall 2015
Student Workbook Options
FOR PRECALCULUS
Available Titles....................................................... page 1
Workbook Options by Feature ................................ page 3
Explorations and Notes .......................................... page 5
Guided Lecture Notes ............................................ page 9
Guided Notebook.................................................. page 19
Learning Guide ..................................................... page 29
MyNotes .............................................................. page 39
Video Notebook .................................................... page 45
Integrated Review (IR) Worksheets * ................. page 57
*IR Worksheets can be purchased with both an Integrated Review
MyMathLab course or a regular MyMathLab course.
Available Titles
Explorations and Notes
Integrated Review (IR) Worksheets
Schulz © 2014
Precalculus, First Edition (Sample)
Beecher/Penna/Bittinger © 2014/16 Series
College Algebra with Integrated Review, Fifth Edition
Blitzer © 2015 Series
College Algebra with Integrated Review, First Edition
Lial/Hornsby/Schneider/Daniels © 2015 Series
Essentials of College Algebra with Integrated Review, First
Edition
Rockswold © 2016 Series
College Algebra with Integrated Review, First Edition
(Sample)
Sullivan © 2016 Series
College Algebra with Integrated Review, Tenth Edition
Trigsted © 2015 Series
College Algebra with Integrated Review, First Edition
Guided Lecture Notes
Sullivan/Sullivan © 2015 Series
College Algebra: Concepts Through Functions, Third Edition
(Sample)
Precalculus: Concepts Through Functions, A Right Triangle
Approach to Trigonometry, Third Edition
Precalculus: Concepts Through Functions, A Unit Circle
Approach to Trigonometry, Third Edition
Sullivan © 2016 Series
College Algebra, Tenth Edition (Sample)
Trigonometry: A Unit Circle Approach, Tenth Edition
Algebra and Trigonometry, Tenth Edition
Precalculus, Tenth Edition
Guided Notebook
Trigsted © 2015 Series
College Algebra, Third Edition (Sample)
College Algebra Interactive, First Edition
Trigonometry, Second Edition
Algebra & Trigonometry, Second Edition
Learning Guide
Blitzer © 2014 Series
College Algebra, Sixth Edition
College Algebra: An Early Functions Approach, Third Edition
College Algebra Essentials, Fourth Edition
Trigonometry, First Edition (Sample)
Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Precalculus Essentials, Fourth Edition
MyNotes
Lial/Hornsby/Schneider/Daniels © 2013/15 Series
College Algebra, Eleventh Edition
Essentials of College Algebra, Eleventh Edition (Sample)
Trigonometry, Tenth Edition
College Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Video Notebook
Beecher/Penna/Bittinger © 2014/16 Series
College Algebra, Fifth Edition (Sample)
Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Dugopolski © 2015 Series
College Algebra, Sixth Edition
Trigonometry, Fourth Edition (Sample)
College Algebra and Trigonometry, Sixth Edition
1
2
3
Workbook Options
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Side-by-Side
Examples
and Practice
X
X
VideoBased
Examples
X
X
End of
Chapter
Review
X
X
X
X
X
Vocab
Exercises
X
X
Study
Skills
Tips
X
X
X
X
X
Note-taking/
Organizational Tool
X
X
X
X
Student
Checklist
*Binding types: B‐ Bound, LL‐ Loose Leaf **The eText Reference for the Trigsted series is another option, and is essentially a printed version of the eText. If someone is looking for a “workbook” type resource, show
them the Guided Notebook. If someone wants the full eText in printed format, show the eText Reference. Send the eText Reference for “instructor desk copies”.
***IR Worksheets can be purchased with both an Integrated Review MyMathLab course or a regular MyMathLab course. Explorations and Notes (Schulz)
Note-taking guide designed to help
students stay focused and to provide a
framework for further exploration.
Guided Lecture Notes
(Sullivan/Sullivan, Sullivan)
Lecture notes designed to help students
take thorough, organized, and
understandable notes as they watch the
Author in Action videos.
Guided Notebook** (Trigsted)
Interactive workbook that guides students
through the course by asking them to
write down key definitions and work
through important examples for each
section of the eText.
Learning Guide (Blitzer)
This workbook provides additional
practice for each section and guidance for
test preparation.
MyNotes (LHSD)
Note-taking structure for students to use
while they read the textbook or watch
the MyMathLab videos.
Video Notebook (BPB, Dugopolski)
Helps students develop organized notes
as they work along with the videos.
Integrated Review (IR)
Worksheets*** (BPB, Blitzer, LHSD,
Rockswold, Sullivan, Trigsted)
Provide extra practice for every text
section, plus multiple methods problems.
Extra
Examples
Extra
Practice
Problems
Learning
Objectives
LL/B
LL
LL
LL
LL
LL
B
Binding*
4
Explorations and
Notes
Note-taking guide designed to help students stay
focused and to provide a framework for further
exploration.
Includes:
 Learning Objectives
 Extra Practice Problems
 Extra Examples
 End of Chapter Review
 Vocab Exercises
 Note-taking/Organizational Tool
 Student Checklist
Available with the Following Titles:
Schulz © 2014
Precalculus, First Edition (Sample)
5
Chapter 1 Exploration & Notes
Chapter 1 Functions
Explorations & Notes: 1.1 What is a Function?
Definition of a Function
DEFINITION
Function, Domain, Range
is a relation between two sets assigning to each element in the first set exactly
A
element in the second set. The first set is called the
the
of the function, and the second set is called
of the function. The
the
is the variable associated with the domain;
belongs to the range.
EXPLORE Example 1
1.
Explain how, with two values of 1 appearing in the second column, Relation 1 is still a function.
EXPLORE Example 2
2.
Explain why the price of an airplane ticket is not a function of the length of the flight.
EXPLORE Example 3
3.
A plot of the tuition function is shown in Figure 1.2. Explain why the points cannot be connected.
Function Notation
H
ó
f
The
ó
x
L.
of a function is the expression on which the function works.
Copyright © 2014 Pearson Education, Inc.
6
1
H
ó
f
2
Precalculus
The
L.
ó
x
Schulz, Briggs, Cochran
of a function is the expression on which the function works.
EXPLORE Example 4
4.
Explain why f HxL + 1 and f Hx + 1L are different (see QUICK CHECK 3).
EXPLORE Example 5
f Hx+hL
fIx + h M - fHx L
f HxL
=
h
h
-
-
=
h
=
h
h
=
=
h
The Natural Domain of a Function
When a function is given without reference to a specific domain, the
of the function is understood to be
the set of real numbers for which outputs of the function are real numbers; that is, where the function is
EXPLORE Example 6
5.
Explain why the natural domain of g is not the set of all real numbers.
6.
Explain why the natural domain of h is the set of all real numbers.
Copyright © 2014 Pearson Education, Inc.
7
.
Chapter 1 Exploration & Notes
7.
Explain why the natural domain of m is not the set of all real numbers.
Check Your Progress
Upon completing this section, you should
· understand the definition of a function;
· be able to determine whether or not a relation given in words is a function;
· be able to determine whether or not a relation given in numeric form is a function;
· understand and be able to use function notation;
· be able to identify the domain and range of a function.
Copyright © 2014 Pearson Education, Inc.
8
3
Guided Lecture Notes
Lecture notes designed to help students take
thorough, organized, and understandable notes
as they watch the Author in Action videos.
Includes:
 Extra Practice Problems
 Extra Examples
 Side-by-Side Examples and Practice
 Vocab Exercises
 Note-taking/Organization Tool
Available with the Following Titles:
Sullivan/Sullivan © 2015 Series
College Algebra: Concepts Through Functions, Third
Edition (Sample)
Precalculus: Concepts Through Functions, A Right
Triangle Approach to Trigonometry, Third Edition
Precalculus: Concepts Through Functions, A Unit Circle
Approach to Trigonometry, Third Edition
Workbook options
Sullivan © 2016 Series
College Algebra, Tenth Edition (Sample)
Trigonometry: A Unit Circle Approach, Tenth Edition
Algebra and Trigonometry, Tenth Edition
Precalculus, Tenth Edition
9
18
Chapter 1 Functions and Their Graphs
Chapter 1: Functions and Their Graphs
Section 1.1: Functions
A relation is a _________________________________.
If x and y are two elements in these sets and if a relation exists between x and y, then we
say that x __________________ to y or that y _____________ x, and we write________.
What are the four ways to express relations between two sets?
Definition: Let X and Y be two nonempty sets. A function from X into Y is a relation that
associates with each element of X __________________________ of Y.
In other words, for a function, no input has more than one output.
The domain of a function is:
The Range of a function is:
Can an element in the range be repeated in a function? For example, can a function contain
the points (2,4) and (3,4) ? Why or why not?
Example 1*: Determine Whether a Relation Represents a Function
Determine which of the following relations represent a function. If the relation is a function,
then state its domain and range.
(a) Level of
(b)  2,3 ,  4,1 ,  3, 2  ,  2, 1
Unemployment
Rate
Education
No High School
Diploma
7.7%
High School
Diploma
5.9%
Some College
5.4%
College Graduate
(c)
3.4%
 2,3 ,  4,1 ,  3, 2 ,  2, 1
(d)
 2,3 ,  4,3 ,  3,3 ,  2, 1
Copyright © 2015 Pearson Education, Inc.
10
Section 1.1 Introduction to Functions 19
Example 2*: Determine Whether a Relation Represents a Function
Determine whether the following are functions, with y as a function of x.
1
(a) y   x  3
(b) x  2 y 2  1
2
In general, the idea behind a function is its predictability. If the input is known, we can use
the function to determine the output. With “nonfunctions,” we don’t have this predictability.
Sometimes it is helpful to think of a function f as a machine that receives as input a number
from the domain, manipulates it, and outputs the value with certain restrictions:
1. It only accepts numbers from _______________.
2. For each input, there is _____________________.
For a function y  f  x  , the variable x is called the ______________________because it
can be assigned to any of the numbers in the domain. The variable y is called the
_________________ because its value depends x.
Example 3: Illustrate Language Used with Functions
State the name, independent variable, and dependent variable of the functions below.
(a) y  g  x   x  6
(b) y  f  x   2 x  3
(c) p  r  n   n 2
Copyright © 2015 Pearson Education, Inc.
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20
Chapter 1 Functions and Their Graphs
Example 4*: Find the Value of a Function
For the function f defined by f  x   3 x 2  2 x , evaluate:
(a) f  3 
(b) f  x   f  3 
(d)  f  x 
(e) f  x  3 
(c) f   x 
(f)
f  x  h   f ( x)
,h  0
h
Example 4(f) is an example of finding the simplified difference quotient of a function. The
difference quotient is used in calculus to find derivatives. In this class, we will only work on
simplification. Let’s practice a few more of these.
Example 5: Find the Value of a Function
Find the simplified difference quotient of f; that is, find (f)
the functions below.
(a) f  x   2 x  1
f  x  h   f ( x)
, h  0 for each of
h
(b) f  x   2 x 2  5 x  1
Copyright © 2015 Pearson Education, Inc.
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Section 1.1 Introduction to Functions 21
In general, when a function f is defined by an equation x and y, we say that f is given
___________. If it is possible to solve the equation for y in terms of x, then we write
y  f ( x) and say that the function is given _______________.
Example 6*: Implicit Form of a Function
Circle the functions below that are written in their implicit form.
3x  y  5
y  f ( x)  x 2  6
xy  4
The domain is the largest set of real numbers for which f ( x) is a real number. In other
words, the domain of a function is the largest set of real numbers that produce real outputs.
Steps for Finding the Domain of a Function Defined by an Equation
1. Start with the domain as the set of _____________.
2. If the equation has a denominator, exclude any numbers that ___________________.
Why do we have to exclude these numbers?
3. If the equation has a radical of even index, exclude any numbers that cause the expression
inside the radical to be _________________.
Why do we have to exclude these numbers?
Example 7*: Find the Domain of a Function Defined by an Equation
Find the domain of each of the following functions using interval or set-builder notation:
x4
(c) h  x   3  2x
(b) g ( x)  x 2  9
(a) f  x   2
x  2x  3
Tip: When finding the domain of application problems, we must take into account the
context of the problem. For example, when looking at the formula for the area of a circle,
A  r 2 , it does not make sense to have a negative radius or a radius of 0. The domain
would be r | r  0 .
Example 8*: Find the Domain of an Application
A rectangular garden has a perimeter of 100 feet. Express the area, A, of the garden as a
function of the width, w. Find the domain.
Copyright © 2015 Pearson Education, Inc.
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22 Chapter 1 Functions and Their Graphs
Definition: Function Operations
The sum, f  g , is defined by ______________________
Domain of f  g : __________________________
The difference, f  g , is defined by _________________
Domain of f  g : __________________________
The product, f  g , is defined by ____________________
Domain of f  g :___________________________
f
, is defined by _____________________
g
f
:_____________________________
Domain of
g
The quotient,
Example 9: Form the Sum, Difference, Product, and Quotient of Two Functions
For the functions f  x   2 x  4 and g  x   3 x  6, find the following. For parts a – d also
find the domain.
(a)
f
 g  x 
(e)  f  g 1
(b)
f
(f)
 g  x 
f
 g 1
(c)
 f  g  x 
f
(d)    x 
g
(g)
 f  g  1
f
(h)   1
g
Example 10*: Form the Sum, Difference, Product, and Quotient of Two Functions
1
x
For the functions f  x  
and g  x  
, find the following and determine the
x2
x4
domain in each case.
f
(d)    x 
(a)  f  g  x 
(b)  f  g  x 
(c)  f  g  x 
g
Copyright © 2015 Pearson Education, Inc.
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34
Chapter 1 Equations and Inequalities
Chapter 1: Equations and Inequalities
Section 1.1: Linear Equations
A linear equation in one variable is an equation equivalent in form to _______________
where a and b are real numbers and _____.
Why does the definition say a ≠ 0 ? What type of equation would it be if a = 0 ?
To solve an equation means to find all the solutions of the equation that make it true.
Solutions can be written in set notation, called the solution set. One method to solve is to
write a series of equivalent equations. Multiple properties from previous courses can help
with this, including the Addition and Multiplication Properties of Equality along with the
Distributive Property.
Example 1*: Solve Linear Equations
Solve the equations:
(a)
6 + y = 11
(b)
1
x=4
7
(c) 3a − 9 = −24
(d) 3a − 8 = 2a − 15
(e) 12 − 2 x − 3( x + 2) = 4 x + 12 − x
(f)
2
1 3
+v = −
5
2 10
(g) 0.9t − 1.2 = 0.4 + 0.1t
Copyright © 2016 Pearson Education, Inc.
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Section 1.1 Linear Equations 35
Sometimes in solving what ends up as a linear equation, does not begin that way.
Example 2: Solve Equations That Lead to Linear Equations
Solve ( x + 2)( x − 4) = ( x + 3) 2 by simplifying first to see the linear equation.
Example 3: Solve Equations That Lead to Linear Equations
2x
−6
=
− 2 by simplifying first to see the linear equation.
Solve
x+5 x+5
Example 4: Solve Equations That Lead to Linear Equations
2x
−6
=
− 2 by simplifying first to see the linear equation. Why does the solution
Solve
x+3 x+3
to this equation end up being ∅ ?
Many applied problems require the solution of a quadratic equation. Let’s look at one in the
next example.
Copyright © 2016 Pearson Education, Inc.
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36 Chapter 1 Equations and Inequalities
Example 5: Solve Problems That Can Be Modeled by Linear Equations
A total of $15,000 is to be divided between Jon and Wendy, with Jon to receive $2500 less
than Wendy. How much will each receive?
Step 1: Determine what you are looking for.
Step 2: Assign a variable to represent what you are looking for. If necessary, express any
remaining unknown quantities in terms of this variable.
Step 3: Translate the English into mathematical statements. A table can be used to organize
the information. Use the information to build your model.
Step 4: Solve the equation and answer the original question.
Step 5: Check your answer with the facts presented in the problem.
Example 6: Solve Problems That Can Be Modeled by Linear Equations
Sierra, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly
wages of $935 for 50 hours worked. Use the steps for solving applied problems to determine
her regular hourly rate.
Copyright © 2016 Pearson Education, Inc.
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18
Guided Notebook
Interactive workbook that guides students
through the course by asking them to write down
key definitions and work through important
examples for each section of the eText.
Includes:
 Learning Objectives
 Video-Based Examples
 Vocab Exercises
 Note-taking/Organizational Tool
 Student Checklist
Available with the Following Titles:
Trigsted © 2015 Series
College Algebra, Third Edition (Sample)
College Algebra Interactive, First Edition
Trigonometry, Second Edition
Algebra & Trigonometry, Second Edition
Workbook options
19
Section 1.1
Section 1.1 Guided Notebook
Section 1.1 Linear Equations
Work through Section 1.1 TTK
Work through Objective 1
Work through Objective 2
Work through Objective 3
Work through Objective 4
Work through Objective 5
Section 1.1 Linear Equations
1.1 Things To Know
1. Factoring Trinomials with a Leading Coefficient Equal to 1
Can you factor the polynomial b 2  9b  14 ? Try working through a “You Try It” problem or
refer to section R.5 or watch the video.
58
Copyright © 2015 Pearson Education, Inc.
20
Section 1.1
2. Factoring Trinomials with a Leading Coefficient Not Equal to 1.
Can you factor the polynomial 15 x 2  17 x  4 ? Try working through a “You Try It” problem
or refer to section R.5 or watch the video.
Section 1.1 Objective 1 Recognizing Linear Equations
What is the definition of an algebraic expression?
What is the definition of a linear equation in one variable?
59
Copyright © 2015 Pearson Education, Inc.
21
Section 1.1
In the Interactive Video following the definition of a linear equation in one variable, which
equation is not linear? Explain why it is not linear.
Section 1.1 Objective 2 Solving Linear Equations with Integer Coefficients
What does the term integer coefficient mean?
Work through Example 1 and Example 2 in your eText and take notes here:
60
Copyright © 2015 Pearson Education, Inc.
22
Section 1.1
Try this one on your own: Solve the following equation: 3  4( x  4)  6 x  32 and see if
you can get an answer of x 
19
. You might want to try a “You Try It” problem now.
10
Section 1.1 Objective 3 Solving Linear Equations Involving Fractions
What is the definition of a least common denominator (LCD)?
What is the first thing to do when solving linear equations involving fractions?
61
Copyright © 2015 Pearson Education, Inc.
23
Section 1.1
Work through the video that accompanies Example 3 and write your notes here: Solve
1
x +1
(1- x ) = -2
3
2
Try this one on your own: Solve the following equation:
see if you can get an answer of x 
1
1
1
x  ( x  4)  ( x  1) and
5
3
2
25
. You might want to try a “You Try It” problem
19
now.
Section 1.1 Objective 4 Solving Linear Equations Involving Decimals
When encountering a linear equation involving decimals, how do you eliminate the
decimals?
62
Copyright © 2015 Pearson Education, Inc.
24
Section 1.1
Work through the video that accompanies Example 4 and write your notes here:
Solve .1( y  2)  .03( y  4)  .02(10)
Try this one on your own: Solve the following equation: 0.004(9  k )  0.04( k  9)  1 and
see if you can get an answer of x =
331
. You might want to try a “You Try It” problem
9
now.
63
Copyright © 2015 Pearson Education, Inc.
25
Section 1.1
Section 1.1 Objective 5 Solving Equations that Lead to Linear Equations
Work through Example 5 and take notes here: Solve 3a 2  1  (a  1)(3a  2)
Work through Example 6 and take notes here:
2 x
4
3
x2
x2
What is an extraneous solution?
64
Copyright © 2015 Pearson Education, Inc.
26
Section 1.1
12
x  3 1 x


x  x  2 x 1 x  2
(What do you have to do BEFORE you find the lowest common denominator?)
Work through Example 7 and take notes here: Solve
2
Try this one on your own: Solve the following equation:
can get an answer of x 
10
4
4
and see if you
 
x  2x x x  2
2
9
. You might want to try a “You Try It” problem now.
4
65
Copyright © 2015 Pearson Education, Inc.
27
28
Learning Guide
This workbook provides additional practice for
each section and guidance for test preparation.
Includes:
 Learning Objectives
 Extra Practice Problems
 Extra Examples
 Side-by-Side Examples and Practice
 End of Chapter Review
 Study Skills Tips
 Note-taking/Organizational Tool
 Student Checklist
Available with the Following Titles:
Blitzer © 2014 Series
College Algebra, Sixth Edition
College Algebra: An Early Functions Approach, Third Edition
College Algebra Essentials, Fourth Edition
Trigonometry, First Edition (Sample)
Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Precalculus Essentials, Fourth Edition
Workbook options
29
Section 1.1
Angles and Radian Measure
Ever Feel Like You’re Just Going in Circles?
You’re riding on a Ferris wheel and wonder how fast you are traveling. Before
you got on the ride, the operator told you that the wheel completes two full
revolutions every minute and that your seat is 25 feet from the center of the wheel.
You just rode on the merry-go-round, which made 2.5 complete revolutions per
minute. Your wooden horse was 20 feet from the center, but your friend, riding
beside you was only 15 feet from the center. Were you and your friend traveling at
the same rate?
In this section, we study both angular speed and linear speed and solve problems
similar to those just stated.
Objective #1: Recognize and use the vocabulary of angles.
Solved Problem #1
Pencil Problem #1
1a. True or false: When an angle is in standard position,
its initial side is along the positive y-axis.
1a. True or false: When an angle is in standard
position, its vertex lies in quadrant I.
False; When an angle is in standard position, its
initial side is along the positive x-axis.
1b. Fill in the blank to make a true statement: If the
terminal side of an angle in standard position lies on
the x-axis or the y-axis, the angle is called a/an
___________ angle.
1b. Fill in the blank to make a true statement: A
negative angle is generated by a __________
rotation.
Such an angle is called a quadrantal angle.
Objective #2: Use degree measure.
Solved Problem #2
Pencil Problem #2
2. Fill in the blank to make a true statement: An angle
1
of a complete rotation
that is formed by
2
measures _________ degrees and is called a/an
_________ angle.
2.
Fill in the blank to make a true statement: An angle
1
of a complete rotation
that is formed by
4
measures _________ degrees and is called a/an
_________ angle.
Such an angle measures 180 degrees and is called a
straight angle.
Copyright © 2014 Pearson Education Inc.
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1
Trigonometry 1e
Objective #3: Use radian measure.
Solved Problem #3
3.
A central angle, θ, in a circle of radius 12 feet
intercepts an arc of length 42 feet. What is the radian
measure of θ?
Pencil Problem #3
3.
A central angle, θ, in a circle of radius 10 inches
intercepts an arc of length 40 inches. What is the
radian measure of θ?
The radian measure of the central angle, θ, is the
length of the intercepted arc, s, divided by the radius
s
of the circle, r: θ  . In this case, s = 42 feet and
r
r = 12 feet.
s 42 feet
θ 
 3.5
r 12 feet
The radian measure of θ is 3.5.
Objective #4: Convert between degrees and radians.
Solved Problem #4
Pencil Problem #4
4a. Convert 60° to radians.
To convert from degrees to radians, multiply by
π radians
. Then simplify.
180
π radians 60π radians π
60  

 radians
180
3
180 
4a. Convert 135° to radians. Express your answer as a
multiple of π.
4b. Convert −300° to radians.
π radians
300π radians
5π
radians
300  


180
3
180 
4b. Convert −225° to radians. Express your answer as
a multiple of π.
2
Copyright © 2014 Pearson Education Inc.
31
Section 1.1
4c. Convert
π
radians to degrees.
4c. Convert
4
To convert from radians to degrees, multiply by
180
. Then simplify.
π radians
π
180
180
radians 

 45
4
4
π radians
π
2
radians to degrees.
4d. Convert 2 radians to degrees. Round to two
decimal places.
4d. Convert 6 radians to degrees.
180
1080
6 radians 

 343.8
π
π radians
Objective #5: Draw angles in standard position.
Solved Problem #5
5a. Draw the angle θ  
Pencil Problem #5
π
in standard position.
4
Since the angle is negative, it is obtained by a
clockwise rotation. Express the angle as a fractional
part of 2π.

π
4

π
4

5a. Draw the angle θ  
5π
in standard position.
4
1
 2π
8
The angle θ  
π
is
4
clockwise direction.
1
of a full rotation in the
8
Copyright © 2014 Pearson Education Inc.
32
3
Trigonometry 1e
3π
in standard position.
4
Since the angle is positive, it is obtained by a
counterclockwise rotation. Express the angle as a
fractional part of 2π.
3π 3
  2π
4 8
3π
3
is
of a full rotation in the
The angle α 
4
8
counterclockwise direction.
5b. Draw the angle α 
13π
in standard position.
4
Since the angle is positive, it is obtained by a
counterclockwise rotation. Express the angle as a
fractional part of 2π.
13π 13
  2π
4
8
13π
13
5
is
or 1 full rotation in the
The angle γ 
4
8
8
counterclockwise direction. Complete one full
5
of a full rotation.
rotation and then
8
5c. Draw the angle γ 
4
5b. Draw the angle α 
7π
in standard position.
6
5c. Draw the angle γ 
16π
in standard position.
3
Copyright © 2014 Pearson Education Inc.
33
Section 1.1
Objective #6: Find coterminal angles.
Solved Problem #6
Pencil Problem #6
6a. Find a positive angle less than 360° that is
coterminal with a 400° angle.
6a. Find a positive angle less than 360° that is
coterminal with a 395° angle.
Since 400° is greater than 360°, we subtract 360°.
400° − 360° = 40°
A 40° angle is positive, less than 360°, and
coterminal with a 400° angle.
6b. Find a positive angle less than 2π that is coterminal
with a 
Since 

A
π
15
π
15
π
15
6b. Find a positive angle less than 2π that is coterminal
with a 
angle.
π
50
angle.
is negative, we add 2π.
 2π  
π
15

30π 29π

15
15
29π
angle is positive, less than 2π, and
15
coterminal with a 
π
15
angle.
Copyright © 2014 Pearson Education Inc.
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5
Trigonometry 1e
6c. Find a positive angle less than 2π that is coterminal
17π
angle.
with a
3
6c. Find a positive angle less than 2π that is coterminal
31π
angle.
with a 
7
17π
is greater than 4π, we subtract two
3
multiples of 2π.
Since
17π
17π
17π 12π 5π
 2  2π 
 4π 


3
3
3
3
3
5π
angle is positive, less than 2π, and coterminal
3
17π
angle.
with a
3
A
Objective #7: Find the length of a circular arc.
Solved Problem #7
7.
Pencil Problem #7
A circle has a radius of 6 inches. Find the length of
the arc intercepted by a central angle of 45°. Express
arc length in terms of π. Then round your answer to
two decimal places.
7.
A circle has a radius of 8 feet. Find the length of the
arc intercepted by a central angle of 225°. Express
arc length in terms of π. Then round your answer to
two decimal places.
We begin by converting 45° to radians.
45  
π radians
180 

45π radians π
 radians
180
4
Now we use the arc length formula s  rθ with the
radius r = 6 inches and the angle θ 
π
4
radians.
3π
 π  6π
s  rθ  (6 in.)   
in. 
in.  4.71 in.
4
4
2
6
Copyright © 2014 Pearson Education Inc.
35
Section 1.1
Objective #8: Find the area of a sector.
Solved Problem #8
8.
Pencil Problem #8
A circle has a radius of 6 feet. Find the area of the
sector formed by a central angle of 150°. Express the
area in terms of π. Then round your answers to two
decimal places.
8.
A circle has a radius of 10 meters. Find the area of
the sector formed by a central angle of 18°.
Express the area in terms of π. Then round your
answers to two decimal places.
1 2
r θ , θ must be expressed in
2
radians, so we convert 150° to radians.
To use the formula A 
150° = 150° ⋅
π radians
180°
=
150π
5π
radians =
radians
180
6
Now we use the formula with r = 6 feet and
5π
θ=
radians.
6
1
1
 5π 
A = r 2θ = (6) 2 

2
2
 6 
= 15π ≈ 47.12 square feet
The area of the sector is approximately 47.12 square
feet.
Objective #9: Use linear and angular speed to describe motion on a circular path.
Solved Problem #9
9.
Pencil Problem #9
A 45-rpm record has an angular speed of
45 revolutions per minute. Find the linear speed, in
inches per minute, at the point where the needle is
1.5 inches from the record’s center.
9.
A Ferris wheel has a radius of 25 feet. The wheel is
rotating at two revolutions per minute. Find the
linear speed, in feet per minute, of a seat on this
Ferris wheel.
We are given the angular speed in revolutions per
minute: ω = 45 revolutions per minute. We must
express ω in radians per minute.
45 revolutions 2π radians

1 minute
1 revolution
90π radians
90π

or
1 minute
1 minute
ω
Now we use the formula υ  rω .
υ  rω  1.5 in. 
90π
135π in.

 424 in./min
1 min
min
Copyright © 2014 Pearson Education Inc.
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7
Trigonometry 1e
Answers for Pencil Problems (Textbook Exercise references in parentheses):
1a. False
1b. clockwise
2. 90; right
3. 4 radians (1.1 #7)
3π
radians (1.1 #15)
4
4d. 114.59° (1.1 #35)
4a.
5a.
4b. 
(1.1 #47)
6a. 35° (1.1 #57)
6b.
99π
50
5π
radians (1.1 #19)
4
5b.
(1.1 #67)
4c. 90° (1.1 #21)
(1.1 #41)
6c.
11π
7
5c.
(1.1 #69)
7. 10π ft ≈ 31.42 ft (1.1 #73)
8.
5π  15.71 sq m (1.1 #75)
9. 100π ft/min ≈ 314 ft/min (1.1 #106)
8
Copyright © 2014 Pearson Education Inc.
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(1.1 #49)
38
MyNotes
Note-taking structure for students to use while
they read the textbook or watch the MyMathLab
videos.
Includes:
 Extra Examples
 Vocab Exercises
 Note-taking/Organizational Tool
Available with the Following Titles:
Lial/Hornsby/Schneider/Daniels © 2013/15
Series
College Algebra, Eleventh Edition
Essentials of College Algebra, Eleventh Edition (Sample)
Trigonometry, Tenth Edition
College Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Workbook options
39
Section 1.1 Linear Equations
1-1
Chapter 1 Equations and Inequalities
1.1 Linear Equations
■ Basic Terminology of Equations ■ Solving Linear Equations
■ Identities, Conditional Equations, and Contradictions
■ Solving for a Specified Variable (Literal Equations)
Key Terms: equation, solution or root, solution set, equivalent equations, linear equation in
one variable, first-degree equation, identity, conditional equation, contradiction, simple
interest, literal equation, future or maturity value
Basic Terminology of Equations
A number that makes an equation a true statement is called a _________________ or
_________________ of the equation.
The set of all numbers that satisfy an equation is called the _________________
_________________ of the equation.
Equations with the same solution set are _________________ _________________.
Addition and Multiplication Properties of Equality
Let a, b, and c represent real numbers.
If a = b, then a + c = b + c.
That is, the same number may be added to each side of an equation without changing the
solution set.
If a = b and c ≠ 0, then ac = bc.
That is, each side of an equation may be multiplied by the same nonzero number without
changing the solution set. (Multiplying each side by zero leads to 0 = 0.)
Copyright © 2013 Pearson Education, Inc.
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1-2
Chapter 1 Equations and Inequalities
Solving Linear Equations
Linear Equation in One Variable
A linear equation in one variable is an equation that can be written in the form
ax + b = 0,
where a and b are real numbers with a ≠ 0.
EXAMPLE 1 Solving a Linear Equation
Solve 3 ( 2 x − 4) = 7 − ( x + 5) .
EXAMPLE 2 Solving a Linear Equation with Fractions.
Solve
2x + 4 1
1
7
+ x= x− .
3
2
4
3
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41
Section 1.1 Linear Equations
1-3
Identities, Conditional Equations, and Contradictions
EXAMPLE 3 Identifying Types of Equations
Determine whether each equation is an identity, a conditional equation, or a contradiction.
Give the solution set.
(a) −2 ( x + 4) + 3 x = x − 8
(b) 5 x − 4 = 11
(c) 3 ( 3 x − 1) = 9 x + 7
Identifying Types of Linear Equations
1. If solving a linear equation leads to a true statement such as 0 = 0, the equation is an
______________. Its solution set is ______________. (See Example 3(a).)
2. If solving a linear equation leads to a single solution such as x = 3, the equation is
______________. Its solution set consists of ______________. (See Example 3(b).)
3. If solving a linear equation leads to a false statement such as −3 = 7, the equation is a
______________. Its solution set is ______________. (See Example 3(c).)
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1-4
Chapter 1 Equations and Inequalities
Solving for a Specified Variable (Literal Equations)
EXAMPLE 4 Solving for a Specified Variable
Solve for the specified variable.
(a) I = Prt ,
for t
(b) A − P = Prt ,
for P
(c) 3 ( 2 x − 5a ) + 4b = 4 x − 2,
for x
Reflect: How is solving a literal equation for a specified variable similar to solving an
equation? How is solving a literal equation for a specified variable different from solving an
equation?
Copyright © 2013 Pearson Education, Inc.
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Section 1.1 Linear Equations
EXAMPLE 5 Applying the Simple Interest Formula
Becky Brugman borrowed $5240 for new furniture. She will pay it off in 11 months at an
annual simple interest rate of 4.5%. How much interest will she pay?
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1-5
Video Notebook
Helps students develop organized notes as
they work along with the videos.
Includes:
 Learning Objectives
 Extra Practice Problems
 Extra Examples
 Video-Based Examples
Available with the Following Titles:
Beecher/Penna/Bittinger © 2016 Series
College Algebra, Fifth Edition (Sample)
Algebra and Trigonometry, Fifth Edition
Precalculus, Fifth Edition
Dugopolski © 2015 Series
College Algebra, Sixth Edition
Trigonometry, Fourth Edition (Sample)
College Algebra and Trigonometry, Sixth Edition
Workbook options
45
Section 1.1 Introduction to Graphing
Section 1.1 Introduction to Graphing
Plotting Points,  x , y  , in a Plane
Each point  x, y  in the plane is described by an ordered pair. The first number, x,
indicates the point’s horizontal location with respect to the y-axis, and the second number,
y, indicates the point’s vertical location with respect to the x-axis. We call x the first
coordinate, the x-coordinate, or the abscissa. We call y the second coordinate, the
y-coordinate, or the ordinate.
Example 1 Graph and label the points  3, 5  ,  4, 3 ,  3, 4  ,  4,  2  ,  3,  4  ,
 0, 4  ,  3, 0  , and  0, 0  .
Example 2 Determine whether each ordered pair is a solution of the equation
2 x  3 y  18.
a)
 5, 7 
2 x  3 y  18
2

  3

18
10  21
18
_______________
True / False
 5, 7  __________ a solution.
is / is not
b)
 3, 4 
2 x  3 y  18
2

  3

18
6  12
18
_______________
True / False
 3, 4  __________ a solution.
is / is not
Copyright © 2016 Pearson Education, Inc.
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1
2
Section 1.1 Introduction to Graphing
x- and y-Intercepts
An x-intercept is a point  a, 0  . To find a, let y  0 and solve for x.
A y-intercept is a point  0, b  . To find b, let x  0 and solve for y.
Example 3
Graph: 2 x  3 y  18.
 0,
Find the y-intercept:
2

Find the x-intercept:
 3 y  18
2x  3
0  3 y  18
3 y  18
 18
2 x  0  18
2 x  18
y
x

Find a third point:  5,


 3 y  18
2




10  3 y  18
3y 
y
Example 4 Graph: 3x  5 y  10.
3 y  5 y  10
5 y 
y
 10
3
x
5
When x  5, y 
3
5

  2  3  2 
3
When x  0, y  
2  02 
5
3
When x  5, 
 2  3 2 
.
5
x
y
 x, y 
5
1
 5,  1
0
5
5
 0,
.
.

 5, 5
Copyright © 2016 Pearson Education, Inc.
47

,0

Section 1.1 Introduction to Graphing
Graph: y  x 2  9 x  12.
Example 5
x  3 :
y
x  2:


2
9
9

  12
y

 12  24
 3,
2

9
 18  12  26
 2,
x
y
 x, y 
3
24
1
2
0
12
2
26
4
32
5
32
10
2
12
24
 3, 24 
 1,  2 
 0,  12 
 2,  26 
 4,  32 
 5,  32 
10,  2 
12, 24 
 12

The Distance Formula
The distance d between any two points  x1 , y1  and  x2 , y2  is given by
d
 x2  x1    y2  y1 
2
 2, 2 
d
and  3,  6 
b)
 x2  x1    y2  y1 
 3 


.
Find the distance between each pair of points.
Example 6
a)
2
2

  
2
2
  8 
2
d
2

2
and  1, 2 
 x2  x1    y2  y1 
2
  1 

2
 02 
 25  64

 1,  5




Copyright © 2016 Pearson Education, Inc.
48
   5 
2


2
2

2
3
4
Section 1.1 Introduction to Graphing
Example 7 The point  2, 5  is on a circle that has  3,  1 as it center. Find the length of
the radius of the circle.
d
 x2  x1    y2  y1 
d



2
  
2
2 
 5
2
 5
2

2
2

 36
 61  7.8
The Midpoint Formula
If the endpoints of a segment are  x1 , y1  and  x2 , y2  , then the coordinates of the
midpoint of the segment are
 x1  x2 y1  y2 
,

.
2 
 2
Example 8
Find the midpoint of the segment whose endpoints are  4,  2  and  2, 5  .
x x y y 
 1 2 , 1 2 
2 
 2
 4 
5

,



2
2


 2 3 
 , 
 2 2
3

, 

2

The diameter of a circle connects the points  2,  3 and  6, 4  on the circle.
Find the coordinates of the center of the circle.
Example 9
 x  x y  y2 
 1 2 , 1

2 
 2
 2
4


,


2
2


1


, 
2

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Section 1.1 Introduction to Graphing
The Equation of a Circle
The standard form of the equation of a circle with center  h, k  and radius r is
 x  h   y  k 
2
2
 r 2.
Find an equation of the circle having radius 5 and center  3,  7  .
Example 10
 x  h   y  k 
2
h3
 x  3
2
k
 y 

 x  3
2
2
 r2
r 5



2
  52


 y
2

Graph the circle  x  5    y  2   16.
2
Example 11
2
 x  h   y  k   r2
 h, k  center, r radius
2
x 


Center:
2

2
   y  2 2 

 5,
2

Radius:
Copyright © 2016 Pearson Education, Inc.
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5
Section 1.1 Angles and Degree Measure
Section 1.1 – Angles and Degree Measure
Angles

Draw a picture of an example of Ray AB :
Draw a picture of an example of Angle CAB :
Initial Side, Terminal Side, Central Angle, and Intercepted Arc
Angle in Standard Position
Copyright © 2015 Pearson Education, Inc.
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21
22
Chapter 1 Angles and the Trigonometric Functions
Degree Measure of Angles
Definition – Degree Measure
A degree measure of an angle is
Draw an example of each of the following:
Acute Angle
Obtuse Angle
Straight Angle
Right Angle
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Section 1.1 Angles and Degree Measure
Negative Angles
Definition – Coterminal Angles
Angles  and  in standard position are coterminal if and only if
Example – Find two positive angles and two negative angles that are coterminal with
50 .
Solution: 310,670, 410, 770
Definition – Quadrantal Angles
A quadrantal angle is an angle with one of the following measures:
Copyright © 2015 Pearson Education, Inc.
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23
24
Chapter 1 Angles and the Trigonometric Functions
Example – Name the quadrant in which each angle lies.
a. 230
b. 580
c. 1380
Solution: a. Quadrant III; b. Quadrant II; c. Quadrant IV
Minutes and Seconds
Important Concept – Minutes and Seconds
The conversion factors for minutes and seconds are as follows:
1 degree = 60 minutes
1 minute = 60 seconds
1 degree = 3600 seconds
Example – Convert the measure  to decimal degrees. Round to four places.
Solution: 44.2083
Example – Convert the measure 44.235 to degrees-minutes-seconds format.
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Section 1.1 Angles and Degree Measure
Solution: 
Example – Perform the indicated operations. Express answers in degree-minutesseconds format.
a.   
b.   
c.   / 2
Solution: a.  ; b.  ; c. 
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25
56
Worksheets
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plus multiple methods problems.
Includes:
 Extra Practice Problems
 Vocab Exercises
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Available with the Following Titles:
Beecher/Penna/Bittinger © 2014/16 Series
College Algebra with Integrated Review, Fifth Edition
Blitzer © 2015 Series
College Algebra with Integrated Review, First Edition
Lial/Hornsby/Schneider/Daniels © 2015
Essentials of College Algebra with Integrated Review,
First Edition
Rockswold © 2016 Series
College Algebra with Integrated Review, First Edition
(Sample)
Sullivan © 2016 Series
College Algebra with Integrated Review, Tenth Edition
Trigsted © 2015 Series
College Algebra with Integrated Review, First Edition
57
Name:
Course/Section:
Instructor:
1.R.1 Use properties of integer exponents.
Review of Exponents ~ The Product Rule ~ The Power Rule ~ The Power of a Product Rule
STUDY PLAN
Read: Read the assigned section in your worktext or eText.
Practice: Do your assigned exercises in your
Book
MyMathLab
Worksheets
Review: Keep your corrected assignments in an organized notebook and use them to review
for the test.
Key Terms
Exercises 1-5: Use the vocabulary terms listed below to complete each statement.
Note that some terms or expressions may not be used.
base
product rule for exponents
power of a product rule for exponents
exponent
power rule for exponents
exponential notation
1. The ________________ states that for any real number base a and natural number exponents
m and n ,
(a )
m n
= a m ⋅n .
2. A mathematical concept called ________________ is used to indicate repeated multiplication.
3. The ________________ states that for any real number base a and natural number exponents
m and n , a m ⋅ a n = a m +n .
4. The exponential expression 34 has ________________ 3 and ________________ 4.
5. The ________________ states that for any real numbers a and b and natural number exponent
n,
( ab )
n
= a nbn .
Copyright © 2016 Pearson Education, Inc.
58
1
2
CHAPTER 1 INTRODUCTION TO FUNCTIONS AND GRAPHS
Review of Exponents
Write each exponential expression as repeated multiplication.
1.
( −5)
2.
y5
3.
( −6x )
4.
−7 3
2
1. ________________
2. ________________
4
3. ________________
4. ________________
The Product Rule
Multiply.
5.
x 3 ⋅ x5
5. ________________
6.
y6 ⋅ y
6. ________________
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59
NAME:
INSTRUCTOR:
3
7.
a3 ⋅ a4 ⋅ a4
7. ________________
8.
3w 4 ⋅ 7 w3
8. ________________
9.
6 x 3 ⋅ ( −8 x 2 )
9. ________________
10.
−3t 2 ⋅ t 3 ⋅ ( −5t 5 )
10. ________________
The Power Rule
Simplify.
11.
(z )
12.
(x ) ⋅(x )
3 4
2 4
11. ________________
3 3
12. ________________
Copyright © 2016 Pearson Education, Inc.
60
4
CHAPTER 1 INTRODUCTION TO FUNCTIONS AND GRAPHS
The Power of a Product Rule
Simplify.
13.
( 3b )
14.
(x y)
15.
( 6x y )
15. ________________
16.
( −3a b )
16. ________________
17.
( 3st ) ( 4s t )
4
3
5
13. ________________
2
14. ________________
3 2
3 4 3
2 3
4
2
17. ________________
Copyright © 2016 Pearson Education, Inc.
61
NAME:
INSTRUCTOR:
5
Key Terms
Exercises 1-7: Use the vocabulary terms listed below to complete each statement.
Note that some terms or expressions may not be used.
negative integer exponents
quotient rule for exponents
zero power rule
base
undefined
exponent
reciprocal
1. The rule for ________________ states that a − n =
1
.
an
2. The exponential expression 2 −5 has ________________ 2 and ________________ −5.
3. The ________________ states that for any nonzero real number base a, a 0 = 1.
4. The expression 00 is ________________.
5. The ________________ states that for any nonzero real number base a and integer exponents
am
m and n , n = a m−n .
a
6.
a − n is the ________________ of a n .
The Quotient Rule
Divide. Assume that all variables represent nonzero numbers.
1.
59
56
1. ________________
2.
y7
y3
2. ________________
3.
28x6
7x
3. ________________
Copyright © 2016 Pearson Education, Inc.
62
6
CHAPTER 1 INTRODUCTION TO FUNCTIONS AND GRAPHS
The Zero Power Rule
Simplify each expression. Assume that all variables represent nonzero numbers.
4.
90
5.
( −4 )
6.
−50
6. ________________
7.
7x 0
7. ________________
4. ________________
0
5. ________________
Negative Exponents
Simplify each expression using the definition of negative integer exponents. Assume that all
variables represent nonzero numbers.
8.
3− 4
8. ________________
9.
x −1
9. ________________
10.
2 y −6
10. ________________
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63